Models (2) chapter solutions to Q2

[CAKABOGU23]

1.) Is "capital required to write a policy" = All the reasons an insurer needs capital (working capital, rating agency etc) including solvency capital, if any?
So does the statement "Holding solvency capital for a policy will impinge significantly on the rate of return earned on the capital required to write a policy." mean excluding Solvency capital, other reasons for capital can be freely invested?

2.) In a jurisdiction where Solvency capital is a fixed $ amount, can I say the Solvency capital to write a policy = zero?

3.) Is the risk discount rate = rate of return expected by the providers of capital (capital here meaning all the reasons capital is needed)

4.) Is "Pre-required solvency capital" = All the reasons an insurer needs capital Excluding Solvency capital

5.) "The assets supporting the policy reserves earn 6% net of tax" Is the lower than 12% return because these assets cannot be freely invested, similar to solvency capital assets?

6.) For the scenarios on what the solvency capital assets earn: I would have thought scenarios 2 and 3 show why the company should stop writing life business since the total rate of return is lower under both scenarios?

 

[Mark Willder]

Hi

An insurer's available capital is the excess of its assets over its liabilities. The required capital is what the insurer needs to hold, eg to meet its regulatory requirements. So we hope the capital that the insurer has (available capital) is more that it needs (required capital). Frustratingly both available and required capital are often abbreviated as just capital, but it should be clear from the context which is which.

I've answered your questions in turn below.

1) Yes, there are many different ways to measure capital requirements. But whichever measure of required capital we use leads to a cost for the providers of capital. If the insurer's available capital is larger than the required capital, then the excess can be invested freely.

2) I think you are suggesting that the regulator requires the company to hold say 50 million of capital in total rather than an amount per policy. In this case I don't think we can say that the solvency capital per policy is zero. We would need to spread the total capital over the whole business so that it is charged for somewhere. But this sounds beyond anything that SP2 would ask about.

3) Yes, the risk discount rate is the return required by the providers of the capital. The amount of capital will reflect the reasons for capital.

4) In this case yes, the pre-required capital is all the reasons to need capital (eg to cover the initial expenses) before we add on the solvency capital which is mentioned in the next paragraph.

5) Yes, it could be that the assets backing the reserves are investing in say bonds with a low expected return. The return on capital from the insurance contract can be found by calculating the internal rate of return on the profit flows each year in the profit test - the question is saying that this internal rate of return is 12%, ie the insurance contract is quite profitable (premiums are high compared to costs).

6) In scenario 2, the insurer earns a return on capital of 10.3%. In scenario 3 they earn 9.7%. Whether they choose to write this business will depend on whether this return is higher than the insurer's required return. If the required return is 9% then they should write this business. If the required return is 11% then they shouldn't write the business.

I hope the above points help.

Best wishes

Mark

 

[CAKABOGU23]

Hi

An insurer's available capital is the excess of its assets over its liabilities. The required capital is what the insurer needs to hold, eg to meet its regulatory requirements. So we hope the capital that the insurer has (available capital) is more that it needs (required capital). Frustratingly both available and required capital are often abbreviated as just capital, but it should be clear from the context which is which.

I've answered your questions in turn below.

1) Yes, there are many different ways to measure capital requirements. But whichever measure of required capital we use leads to a cost for the providers of capital. If the insurer's available capital is larger than the required capital, then the excess can be invested freely.

2) I think you are suggesting that the regulator requires the company to hold say 50 million of capital in total rather than an amount per policy. In this case I don't think we can say that the solvency capital per policy is zero. We would need to spread the total capital over the whole business so that it is charged for somewhere. But this sounds beyond anything that SP2 would ask about.

3) Yes, the risk discount rate is the return required by the providers of the capital. The amount of capital will reflect the reasons for capital.

4) In this case yes, the pre-required capital is all the reasons to need capital (eg to cover the initial expenses) before we add on the solvency capital which is mentioned in the next paragraph.

5) Yes, it could be that the assets backing the reserves are investing in say bonds with a low expected return. The return on capital from the insurance contract can be found by calculating the internal rate of return on the profit flows each year in the profit test - the question is saying that this internal rate of return is 12%, ie the insurance contract is quite profitable (premiums are high compared to costs).

6) In scenario 2, the insurer earns a return on capital of 10.3%. In scenario 3 they earn 9.7%. Whether they choose to write this business will depend on whether this return is higher than the insurer's required return. If the required return is 9% then they should write this business. If the required return is 11% then they shouldn't write the business.

I hope the above points help.

Best wishes

Mark

Thanks so much Mark.

2.) Yes, 50 million in total regardless of however much new business is added.

I'm thinking about how an embedded value model will be set up under such a jurisdiction since the profit flow model should allow for solvency capital.
Regardless of how many policies are written, there is no marginal addition to the 50 million so I was thinking to set the solvency capital to zero in the EV model.

Somewhat related to the above:
In Section 1.4 Capital requirements "The capital requirement should also allow for any supervisory minimum solvency capital needed"
In a Solvency II jurisdiction, would "supervisory minimum" refer to the MCR?

 

[CAKABOGU23]

Does "Normal investments" refer to the investment of the solvency capital assets?
Secondly, please confirm "normal" is not referring to whether the assets can be freely invested.

 

[Mark Willder]

Thanks so much Mark.

2.) Yes, 50 million in total regardless of however much new business is added.

I'm thinking about how an embedded value model will be set up under such a jurisdiction since the profit flow model should allow for solvency capital.
Regardless of how many policies are written, there is no marginal addition to the 50 million so I was thinking to set the solvency capital to zero in the EV model.

Somewhat related to the above:
In Section 1.4 Capital requirements "The capital requirement should also allow for any supervisory minimum solvency capital needed"
In a Solvency II jurisdiction, would "supervisory minimum" refer to the MCR?

Hi

These ideas are beyond the SP2 syllabus. The Core Reading is deliberately avoiding giving definitive answers about what must be done as requirements will vary between countries, but SP2 is not country specific.

In subject SA2 we look at EV and the treatment of required capital in more detail. Any capital held by the insurer would typically be included in the EV (for example in an EEV or MCEV calculation described in Subject SA2). The value of the capital included in the EV would typically be reduced from its face value to reflect the fact that it is locked in and so not available to be passed on to the shareholders now.

Subject SP2 does not refer to Solvency II - this is covered in SA2. The insurer should at least allow for the MCR as this is the minimum amount of capital it is required to hold. However, it may feel that in practice it really needs to hold a higher level of capital than this and will include that in its models.

Best wishes

Mark

 

[Mark Willder]

Does "Normal investments" refer to the investment of the solvency capital assets?
Secondly, please confirm "normal" is not referring to whether the assets can be freely invested.

Hi

The point being made here is that an investor has a choice between investing their assets in the normal way (whatever that may be, perhaps buying shares on the stock market) or instead investing by providing capital to the insurer. The question tells us that the insurer earns a return of 12% on its capital, so the investor should only provide capital to the insurer if this is better than what it would typically earn on its normal investment strategy.

Best wishes

Mark

 

[CAKABOGU23]

Hi Mike,
I'm preparing for subject SA2 but wanted to revisit the foundational topics in SP2 (which I sat in 2015).